1. If the annual demand for a product is 350,000 units, then the annual carrying cost rate is 25 percent of the cost of the unit, the product costs $14.75 per unit to purchase, and each time the product is ordered the related ordering cost is $53.00.
a. What is EOQ?
b. What is the Total Cost at the EOQ?
c. How much would the Total Cost increase if the order quantity must be 2,500 units because of standard shipping-container size?
2. The information system department of a local university buys paper for its copier machine frequently. Andrea Webb, the office manager, would like to determine the best quantity to order each time and order is placed. She has estimated that the ordering cost is $12 each time an order is placed. The monthly demand for paper is 135 reams (500 sheets to a ream). The cost of paper is $6.50 per ream, and the carrying cost is 25 percent of the paper cost per month. How many reams should be ordered at a time, and what is expected average inventory level for copier paper?
3. The production rate of final assembly is 2,400 digital video discs (DVDs) per day. After DVDs are assembled, they go directly to finished-goods inventory. Customers demand averages 1,300 DVDs per day, or about 325,000 per year. It costs $700 to set up the assembly line for the DVDs, the cost per DVD is $2.30, and the carrying cost rate is 30 percent of product cost per year.
a. How many DVDs should be in a production batch at final assembly?
b. What is the annual Total Cost at the EOQ?
4. Louisiana Oil Refining buys crude oil on a long-term supply contract for $38 per barrel. When shipments of crude oil are made to the refinery, they arrive at the rate of 12,000 barrel per day. Louisiana Oil uses the oil at a rate of 5,000 barrels per day and plans to purchase 600,000 barrels of crude oil next year. If the carrying cost is 30 percent of acquisition cost per unit per year and the ordering cost is $11,600 per order:
a. What is the EOQ for the crude oil?
b. What is the Total Cost at the EOQ?
c. How many days’ worth demand are supported by each order of crude oil?
d. How much needed storage capacity is expected for the crude oil?
5. A grocery store orders paper grocery bags from a distributor. The store uses about 2,300 cases of bags per year, and its ordering cost is $65 per order. The stores carrying cost rate is 35 percent of acquisition cost. The distributor has the following pricing structure for cases of bags: 1-49 cases, $129.95 per case; 50-249, $127.95 per case; 250-999, $126.95 per case; 1000 +, $125.95 per case.
a. How many cases of bags should the store order each time?
b. What would be the resulting total inventory cost per year (ordering plus carrying plus material)?
c. How many orders per year should be expected?
d. What is the expected maximum inventory level of paper bags (in cases)?
e. If the store has only enough storage space for 200 cases of bags, how many should it order each time?
6. A fuel distributor near the Tuledo airport is the sole vendor of jet fuel at the airport. Annual demand for jet fuel is 5,202,000 gallons, and daily demand averages 17,000 gallons. The distributor operates 306 days per year. The distributor orders jet fuel from a refinery that is several hundred miles away. The refinery will deliver fuel to the distributor at the rate of 44,000 gallons per day, although a smaller quantity can be delivered to complete an order. The distributor’s ordering cost is $1,500 per order, and the annual carrying cost rate is 30 percent of the acquisition cost. The refinery has the following pricing structure: 10,000-44,000 gallons is $3.40 per gallon; 44,001-88,000 gallons is $3.30 per gallon; 88,000+ is $3.20 per gallon. Orders of less than 10,000 gallons are not accepted.
a. How many gallons of jet fuel should the distributor order each time?
b. What would be the total resulting inventory cost per year (ordering plus carrying plus material)?
c. How many orders per year should be expected?
d. How many days will it take to receive the entire order if the first shipment arrives the day after the order is placed?
e. What should be the maximum inventory level that is expected?